Problem: Simplify; express your answer in exponential form. Assume $z\neq 0, y\neq 0$. $\dfrac{{z^{2}}}{{(zy^{3})^{2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{2}}$ to the exponent ${1}$ . Now ${2 \times 1 = 2}$ , so ${z^{2} = z^{2}}$ In the denominator, we can use the distributive property of exponents. ${(zy^{3})^{2} = (z)^{2}(y^{3})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{z^{2}}}{{(zy^{3})^{2}}} = \dfrac{{z^{2}}}{{z^{2}y^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{2}}}{{z^{2}y^{6}}} = \dfrac{{z^{2}}}{{z^{2}}} \cdot \dfrac{{1}}{{y^{6}}} = z^{{2} - {2}} \cdot y^{- {6}} = y^{-6}$.